Dealing with Ideologically Inflexible Clients

Calling all business consultants, designers, life coaches, etc! Have you ever had a client who wanted things to be different (more revenue, a larger client base, a new look for their branding, etc) but was unwilling to make the changes necessary for that to happen? Or had a client involved in a brainstorming process where their rigidity of thinking held up the entire group? How did you cope? What did you do? (Assume dropping the client is an absolute last resort) I'm looking for work-arounds, conversational techniques, coaching ideas, anything that could help get a client unstuck, gain perspective, and/or shift their perceptions. Someone recently recommended the Art of Thinking as a way to identify different thinking styles and work with them, but I feel like I need to cast a wider net here. Thank you, HiveMind!